Abstract
The study of the Burgers equation with a random force leads via a Hopf-Cole type transformation to a stochastic heat equation having a white noise with spatial parameters type potential. The latter can be studied by means of a general model of directed polymers in random environments with two point random potentials. These models exhibit a Gaussian behavior at large times and have certain stationary distributions which yield the corresponding results for the above stochastic heat and Burgers equations.
| Original language | English |
|---|---|
| Pages (from-to) | 29-65 |
| Number of pages | 37 |
| Journal | Probability Theory and Related Fields |
| Volume | 108 |
| Issue number | 1 |
| DOIs | |
| State | Published - May 1997 |